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user1118321's answer will provide you the correct answer, though it is more general than necessary. Since we're dealing with a right triangle, the easiest solution is to use the definition of the tangent function: tan(α) = A / B Substituting half the height of the screen, the z coordinate of the camera, and half the vertical field of view gets us: ...


Check out the Law of Cosines. It allows you to calculate any side or angle in a triangle if you have the opposite 2 angles or sides. Or alternately, use the law of sines (described at the bottom of the above link). In your case, you know that vertical field of view is 45 degrees and that the base side you want is the height of the screen. You can think of ...

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